The Nigeria international – who represented his country at last year’s World Cup – has impressed in Serie A this term, earning much praise for his physically imposing playing style in the middle of the pitch.
Liverpool were interested in a January move for his signature, but despite talk of a swap deal involving Fabio Borini, the Rome giants held firm to keep their man.
However, since then Onazi has struggled for game time at the Stadio Olimpico, and the sky blue-clad side have altered their stance.
This has lured Liverpool back in, while West Ham are also in the battle.
Lazio are demanding around £7.1m for the 22-year-old.
Onazi has been with the Serie A side since 2011, when he joined them from My People in Nigeria.